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Write 206 in base 7

413_7

Step-by-step explanation:

Convert the following to base 7:

206_10

Hint: | Starting with zero, raise 7 to increasingly larger integer powers until the result exceeds 206.

Determine the powers of 7 that will be used as the places of the digits in the base-7 representation of 206:

Power | \!\(\*SuperscriptBox[\(Base\), \(Power\)]\) | Place value

3 | 7^3 | 343

2 | 7^2 | 49

1 | 7^1 | 7

0 | 7^0 | 1

Hint: | The powers of 7 (in ascending order) are associated with the places from right to left.

Label each place of the base-7 representation of 206 with the appropriate power of 7:

Place | | | 7^2 | 7^1 | 7^0 |  

| | | ↓ | ↓ | ↓ |  

206_10 | = | ( | __ | __ | __ | )_(_7)

Hint: | Divide 206 by 7 and find the remainder. The remainder is the first digit from the right.

Determine the value of the first digit from the right of 206 in base 7:

206/7=29 with remainder 3

Place | | | 7^2 | 7^1 | 7^0 |  

| | | ↓ | ↓ | ↓ |  

206_10 | = | ( | __ | __ | 3 | )_(_7)

Hint: | Divide the whole number part of the previous quotient, 29, by 7 and find the remainder. The remainder is the next digit.

Determine the value of the next digit from the right of 206 in base 7:

29/7=4 with remainder 1

Place | | | 7^2 | 7^1 | 7^0 |  

| | | ↓ | ↓ | ↓ |  

206_10 | = | ( | __ | 1 | 3 | )_(_7)

Hint: | Divide the whole number part of the previous quotient, 4, by 7 and find the remainder. The remainder is the last digit.

Determine the value of the last remaining digit of 206 in base 7:

4/7=0 with remainder 4

Place | | | 7^2 | 7^1 | 7^0 |  

| | | ↓ | ↓ | ↓ |  

206_10 | = | ( | 4 | 1 | 3 | )_(_7)

Hint: | Express 206_10 in base 7.

The number 206_10 is equivalent to 413_7 in base 7.

206_10 =413_7